# Category:Inductive Classes

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This category contains results about Inductive Classes.

Definitions specific to this category can be found in Definitions/Inductive Classes.

Let $A$ be a class.

Then $A$ is **inductive** if and only if:

\((1)\) | $:$ | $A$ contains the empty set: | \(\ds \quad \O \in A \) | ||||||

\((2)\) | $:$ | $A$ is closed under the successor mapping: | \(\ds \forall x:\) | \(\ds \paren {x \in A \implies x^+ \in A} \) | where $x^+$ is the successor of $x$ | ||||

That is, where $x^+ = x \cup \set x$ |

## Subcategories

This category has the following 6 subcategories, out of 6 total.

### G

### I

### M

### S

### T

## Pages in category "Inductive Classes"

The following 2 pages are in this category, out of 2 total.